Method for determining sensor network delay time

ABSTRACT

A method for evaluating performance of a sensor network. The method includes selecting, a sensor distribution pattern for a geographical region and determining a location for a base station. A plurality of sensor clusters are generated, each sensor cluster being formed by one of a first and second grouping mechanism. Further, the method allocates, for each sensor a time-slot within a time-frame to transmit a data packet from the sensor to the base station, and evaluates the performance of the first grouping mechanism and the second grouping mechanism for the selected sensor distribution pattern and base station location, by computing at least a ratio of delivered data packets to the base station to a total energy consumption, and a first delay and a second delay incurred by each data packet.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of Ser. No. 15/059,370, nowallowed, having a filing date of Mar. 3, 2016, which claims benefit ofpriority to U.S. provisional application No. 62/141,058, having a filingdate of Mar. 31, 2015, which is incorporated herein by reference in itsentirety.

BACKGROUND

The background description provided herein is for the purpose ofgenerally presenting the context of the disclosure. Work of thepresently named inventors, to the extent the work is described in thisbackground section, as well as aspects of the description that may nototherwise qualify as prior art at the time of filing, are neitherexpressly nor impliedly admitted as prior art against the presentdisclosure.

Provisioning of quality of service (QoS) is the ultimate goal for anywireless sensor network (WSN). Several factors can influence thisrequirement such as the adopted cluster formation algorithm. Almost allWSNs are structured based on grouping the sensors nodes into clusters.Not all contemporary cluster formation and routing algorithms aredesigned to provide/sustain certain QoS requirement such as delayconstraint. Another fundamental design issue is that, these algorithmsare built and tested under the assumption of uniformly distributedsensor nodes. However, this assumption is not always true. In someindustrial applications and due to the scope of the ongoing monitoringprocess, sensors are installed and condensed in certain areas, whilethey are widely separated in other areas. Also unlike the randomdeployment distributions, there are several applications that needdeterministic deployment of sensors like grid distribution.

A wireless sensor network (WSN) includes spatially distributed,autonomous, and battery-powered sensors to monitor physical orenvironmental conditions, such as temperature, sound, vibration,pressure, motion or pollutants and to cooperatively pass their datathrough the network to a main location (i.e., base station or sink).Recently, as described by I. F. Akyildiz et al. in “Wireless sensornetworks: a survey”, Elsevier J. Computing. Networks, (2002) 393-433,which is incorporated herein by reference in its entirety, wirelesssensor networks have been used in a wide range of applications such asbattlefield surveillance in military applications, industrial processautomation (monitoring and controlling), meteorological areas, homeappliances, and health applications.

However, wireless sensor nodes have limited resources in terms ofprocessing, storage, and communication capabilities and using existingrouting protocols for ad-hoc networks is not efficient. Therefore,power-aware routing protocols such as those described by A. Kemal et.al. in “A survey on routing protocols for wireless sensor networks”,Elsevier J. Ad Hoc Netw. 3 (2005) (2005) 325-349, by K. Pavai in “Studyof routing protocols in wireless sensor networks, in: Advances inComputing, Control, & Telecommunication Technologies”, ACT '09.International Conference, 2009, and by J. N. Al-Karaki in “Routingtechniques in wireless sensor networks: a survey”, IEEE Wireless Commun.(2004), each of which is incorporated herein by reference in theirentirety, have been proposed and several surveys and comparison studieshave been conducted.

All these studies have explored the performance of routing protocolsunder the assumption of uniformly distributed or deployed sensor nodesin the area of interest. However, this assumption is not always trueespecially in industrial networks where the ongoing applicationsdetermine the location of a sensor node to monitor and control aspecific region or a machine, whereas in military applications it mightbe deployed by throwing them from a plane that may resemble a normaldistributed scenario.

A few non-uniform deployment strategies have been studied in pastpublished works. However, none of them have studied the impact of sensordistributions on WSN routing protocols. A primary focus of the abovestated works was on increasing the total data capacity by onlyconsidering the energy spent on the data transmission. Further, J. Lian,et. al. in “Data capacity improvement of wireless sensor networks usingnon-uniform sensor distribution”, Int. J. Distrib. Sen. Netw. 2 (2)(2006) 121-145, incorporated herein by reference in its entirety,presented a finding that in a uniformly distributed homogeneous WSN witha static base station, after the lifetime of the network is over, up to90% of the total initial energy remains unused. The authors proposed anon-uniform sensor distribution strategy by adding more nodes to theheavier energy load area, and thereby maximizing the network lifetime bybalancing the energy consumption over nodes. The simulation resultsshowed that the strategy can increase the total data capacity by anorder of magnitude.

Wu et al. in “On the Energy Hole Problem of Non-uniform NodeDistribution in Wireless Sensor Networks”, Third IEEE Int'l Conf. MobileAd-hoc and Sensor Systems, MASS '06, October 2006, pp. 180-187, andincorporated herein by reference in its entirety, address the energyhole problem in WSNs with non-uniform node distribution. The authorsinvestigated the theoretical aspects of the non-uniform nodedistribution strategy, which aim to avoid the energy hole around thesink. They assumed that each sensor generates data for each datacollection period, which may not be true for highly dense WSNs. Theyprovided a non-uniform node distribution strategy, which makes thenumber of nodes increases with geometric proportion from the outer partsto the inner parts of the network, which looks like normal distribution.Simulation experiments demonstrated that when the network lifetime hasended, the nodes in the inner parts of the network achieve nearlybalanced energy depletion, and only less than 10% of the total energy iswasted. Liu et al. proposed in their work “Power-aware node deploymentin wireless sensor networks”, Int. J. Distrib. Sen. Netw. 3 (2007)225-241, incorporated herein by reference in its entirety, a non-uniformdeployment scheme based on a general sensor application model. Theyderived a function to determine the number of nodes as a function of thedistance from the sink. They also assumed that each sensor is requiredto report the data back to the sink. Simulations show that their methodcan enhance the network lifetime.

All these non-uniform deployment strategies focused on accuratelycontrolling the location of sensors in the network domain for achievinga higher lifetime. In some real applications, it is hard to strictlycontrol the number of nodes in a given domain, e.g., the sensors thatare dropped from a helicopter or a low-flying unmanned aerial vehicle.Zou and Chakraborty suggested in “Uncertainty-aware andcoverage-oriented deployment for sensor networks”, J. Parallel Distrib.Comput. 64 (2004) 788-798, incorporated herein by reference in itsentirety, the placement of airdropped sensors as 2D Gaussiandistribution without giving any specific results.

Wang et al. in “Coverage and lifetime optimization of wireless sensornetworks with Gaussian distribution”, IEEE Trans. Mob. Comput. 7 (12)(2008), incorporated herein by reference in its entirety argued that anappropriate strategy can be employed when dropping sensors from a planeto have the standard deviation of the 2D Gaussian distribution. Forinstance, this can be performed by controlling the height of the planeor using some specific devices to eject sensors with different circularangles. Therefore, distribution of sensors could satisfy 2D Gaussiandistribution and follows a predefined standard deviation with the centerpoint at the drop point of the helicopter. As such, it enables sensorsto have a higher probability to be deployed near the drop point than theuniform deployment. The benefit in doing so, is that it relaxes theenergy-hole problem and increases the WSN lifetime. Further, the authorsinvestigated the Gaussian distribution as a deployment strategy in WSNs.Their study was focused on two important design factors: deploymentstrategy, and the lifetime and coverage. In this work, they haveprovided theoretical formulations for lifetime and coverage in a WSNbased on 2D Gaussian distribution. Two types of dispersions areconsidered, σx=σy and σx≠σy. The analytical model captures the intrinsicproperties of the coverage and the lifetime by using various parameters.The authors showed that the Gaussian distribution can effectivelyincrease the lifetime. The analytical results could serve as the WSNdesign guideline. For this purpose, they have developed two algorithmsto compute the optimal deployment strategy and show that the optimaldeployment strategy can be obtained in a polynomial time complexity.Although they came out of the general nature of previous studies byincluding a non-uniform distribution in their study, their study did notdescribe or suggest, at least, the impact of Gaussian distributiondeployment on the existence WSN routing protocols.

Wu and Chen proposed in “A Partition-Based Hybrid Clustering RoutingProtocol for WSN”, in: Proc. IEEE International Conference of InternetTechnology and Applications, iTAP, August 2011, and incorporated hereinby reference in its entirety, a partition-based hybrid clusteringrouting protocol (named PHCR). To address the problem that thecluster-heads are distributed unevenly in the network, they divided thenetwork monitored area into several sectors through the partitionalgorithm. In the first round, the sensor node which is the nearest tothe area center is selected as the cluster heads by the sink node, andthe other nodes in each sector become the member nodes. The sensor nodewhich is the second closest to the sector center is selected as thecluster head for the second round. After the second round, the clusterhead of the next round is chosen by the prior cluster head of its owncluster. Simulation results showed that PHCR has improved the networklifetime effectively.

Sara et al. described in “Effect of node distributions on lifetime ofWireless Sensor Networks”, in: Industrial Electronics (ISIE), 2010 IEEEInternational Symposium on, 4-7 Jul. 2010, pp. 434-439, and incorporatedherein by reference in its entirety, the effect of node distributions onlifetime of WSNs. However their work focuses on prolonging the networklifetime by investigating different node deployments including bothgeometric and uniform. Geometric distributions are represented by startopologies with different variations of number of star brunches andnumber of nodes in each brunch. It was ascertained in this work that the3×33 star resulted in the highest network lifetime for a 100×100 m andfurthermore it produced 4612 cycles, exceeding random distributionsresults by 1212 cycles.

Peng et. al. in “Impacts of sensor node distributions on coverage insensor networks”, Elsevier J. Parallel Distrib. Comput. (2011), andincorporated herein by reference in its entirety, studied the impact ofsensor node distributions on coverage in sensor networks as the coverageis an important QoS measurement for many sensor network applications.They showed the impact on network coverage by adopting different sensornode distributions through both analytical and simulation studies. Theyobserved that assuming different sensor distributions may lead tosignificant differences in coverage estimation. They adopted adistribution-free approach to study network coverage, in which noassumption of probability distribution of sensor node locations isneeded. Although they only studied the network coverage, they claimedthat their methodology can be generalized and extended to estimate othersensor network performance metrics.

Lin et al. in “Balancing energy consumption with mobile agents inwireless sensor networks, Elsevier J. Future Generation. Comput. Syst.28 (2012) 446-456”, incorporated herein by reference in its entirety,investigated the problem of energy consumption balance during datacollection in WSNs and they showed that for a sensor network withuniform node distribution and constant data reporting, balancing theenergy of the whole network cannot be realized when the distribution ofdata among sensor nodes is unbalanced. The authors also showed that inorder to obtain better performance, the cluster structure is betterformed based on cellular topology taking into consideration the energybalancing of inter-cluster and intra-cluster environments.

Hock et al. in “Energy Efficient Routing for Wireless Sensor Networkswith Grid Topology”, in: IFIP International Federation for InformationProcessing, 2006, pp. 834-843, incorporated herein by reference in itsentirety, performed intensive survey and classification for the previousworks on cluster-based WSN. They presented a taxonomy and generalclassification of published clustering schemes. Also they demonstrateddifferent clustering algorithms for WSNs; highlighting their objectives,features, complexity; and comparing these clustering algorithms based onmetrics such as convergence rate, cluster stability, clusteroverlapping, location awareness and support for node mobility.

Other studies on WSN clustering by Abbasi and Younis (described in “Asurvey on clustering algorithms for wireless sensor networks”, ElsevierJ. Comput. Commun. 30 (2007) 2826-2841, and incorporated herein byreference in its entirety) and by Liu et. al. (described in “A survey onclustering routing protocols in wireless sensor Netw., Sensors (2012)11113-11153, and incorporated herein by reference in its entirety)highlighted the challenges in clustering a WSN, and discussed the designrationale of the different clustering approaches, several key issuesthat affect the practical deployment of clustering techniques in sensornetwork applications. The able works systematically analyzed a few ofWSN clustering routing protocols and compared these different approachesaccording to their taxonomy and several significant metrics, such asinter and intra-cluster routing, cluster head election, mobility, anduniformity of cluster sizes.

Liu et al. took another direction and analyzed the communication energyconsumption of the clusters and the impact of node failures on coveragewith different densities. A distributed algorithm that considers bothenergy and topological features of the sensor network was proposed. Itaimed at selecting the smallest set of nodes with more neighbors as thecluster heads to cover the whole. The algorithm requires neither timesynchronization nor knowledge of a node's geographic location.Simulation results showed that the proposed algorithm can prolong thenetwork lifetime and improve network coverage effectively in comparisonwith EECF, LEACH. However, selecting small set of cluster heads leads tolarger cluster size and hence higher intra-cluster delay.

Accordingly, the present disclosure provides for a framework to evaluatethe performance of wireless sensor networks and further determine theimpact of distributions of sensor deployments.

SUMMARY

An aspect of the present disclosure provides for a method of operating acomputer system to determine the performance of a wireless sensornetwork, the method comprising: selecting, a sensor distribution patternfor a geographical region where the sensors are to be deployed;determining a location for a base station in the geographical region;generating by circuitry, a plurality of sensor clusters, each sensorcluster of the plurality of sensor clusters being formed by one of afirst grouping mechanism and a second grouping mechanism, the firstgrouping mechanism forming the sensor cluster based on a strength of asignal transmitted by each sensor, that is received by the base station,and the second grouping mechanism forming the sensor cluster based on alocation of the sensor and an energy level of the sensor; allocating,for each sensor included in the generated sensor cluster, a time-slotwithin a time-frame corresponding to the sensor cluster, the time-slotbeing utilized for transmitting a data packet from the sensor to thebase station; and evaluating by circuitry, the performance of the firstgrouping mechanism and the second grouping mechanism for the selectedsensor distribution pattern and base station location, by computing atleast a ratio of delivered data packets to the base station to a totalenergy consumption, and a first delay and a second delay incurred byeach data packet.

Another aspect of the present disclosure provides for a non-transitorycomputer readable medium having stored thereon a program that whenexecuted by a computer causes the computer to execute a method todetermine the performance of a wireless sensor network, the methodcomprising: selecting, a sensor distribution pattern for a geographicalregion where the sensors are to be deployed; determining a location fora base station in the geographical region; generating by circuitry, aplurality of sensor clusters, each sensor cluster of the plurality ofsensor clusters being formed by one of a first grouping mechanism and asecond grouping mechanism, the first grouping mechanism forming thesensor cluster based on a strength of a signal transmitted by eachsensor, that is received by the base station, and the second groupingmechanism forming the sensor cluster based on a location of the sensorand an energy level of the sensor; allocating, for each sensor includedin the generated sensor cluster, a time-slot within a time-framecorresponding to the sensor cluster, the time-slot being utilized fortransmitting a data packet from the sensor to the base station; andevaluating the performance of the first grouping mechanism and thesecond grouping mechanism for the selected sensor distribution patternand base station location, by computing at least a ratio of delivereddata packets to the base station to a total energy consumption, and afirst delay and a second delay incurred by each data packet.

According to another aspect of the present disclosure is provided adevice comprising: circuitry configured to select a sensor distributionpattern for a geographical region where the sensors are to be deployed,determine a location for a base station in the geographical region,generate a plurality of sensor clusters, each sensor cluster of theplurality of sensor clusters being formed by one of a first groupingmechanism and a second grouping mechanism, the first grouping mechanismforming the sensor cluster based on a strength of a signal transmittedby each sensor, that is received by the base station, and the secondgrouping mechanism forming the sensor cluster based on a location of thesensor and an energy level of the sensor, allocate for each sensorincluded in the generated sensor cluster, a time-slot within atime-frame corresponding to the sensor cluster, the time-slot beingutilized for transmitting a data packet from the sensor to the basestation, and evaluate the performance of the first grouping mechanismand the second grouping mechanism for the selected sensor distributionpattern and base station location, by computing at least a ratio ofdelivered data packets to the base station to a total energyconsumption, and a first delay and a second delay incurred by each datapacket.

The foregoing paragraphs have been provided by way of generalintroduction, and are not intended to limit the scope of the followingclaims. The described embodiments together, with further advantages,will be best understood by reference to the following detaileddescription taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

Various embodiments of this disclosure that are provided as exampleswill be described in detail with reference to the following figures,wherein like numerals reference like elements, and wherein:

FIG. 1 illustrates an exemplary cluster-head formation;

FIGS. 2A-2D illustrate according to an embodiment sensor node deploymentfor different distributions;

FIGS. 3A-3D illustrate according to an embodiment sensor node deploymentfor different distributions;

FIG. 4 depicts an exemplary graph illustrating an expected relationshipbetween inter-cluster and intra-cluster delay;

FIG. 5 depicts an exemplary bar graph depicting the performance of LEACHwith different sensor distributions and base station locations;

FIG. 6 depicts an exemplary graph depicting the performance of theLEACH-C with different sensor distributions and base station locations;

FIGS. 7A-7D depicts exemplary graphs depicting average packet energy fordifferent data rates for LEACH and LEACH-C;

FIG. 8 depicts according to an embodiment, an exemplary graphillustrating average inter and intra-cluster delay for different sensordistributions;

FIG. 9 depicts according to another embodiment, an exemplary graphillustrating average inter and intra-cluster delay for different sensordistributions;

FIG. 10 depicts a graph illustrating intra-cluster delay cumulativedistribution function (CDF) according to an embodiment;

FIG. 11 depicts according to an embodiment, an exemplary graphillustrating inter-cluster delay CDF;

FIG. 12 depicts a zoomed version of the inter-cluster CDF of FIG. 11;

FIG. 13 depicts a graph illustrating intra-cluster CDF corresponding toa fixed spreading factor; and

FIG. 14 illustrates an exemplary block diagram of a computing device.

DETAILED DESCRIPTION OF EMBODIMENTS

Exemplary embodiments are illustrated in the referenced figures of thedrawings. It is intended that the embodiments and figures disclosedherein are to be considered illustrative rather than restrictive. Nolimitation on the scope of the technology and of the claims that followis to be imputed to the examples shown in the drawings and discussedherein.

In what follows a presented a detailed description of the LEACH andLEACH-C protocols used herein to determine the performance of wirelesssensor networks. LEACH is Low Energy Adaptive Clustering Hierarchy(LEACH) protocol. LEACH is a clustering-based communication protocolthat forms clusters of the sensor nodes based on the received signalstrength and use local cluster heads as routers to the sink. In doingso, the LEACH incurs the advantageous ability of saving energy since thetransmissions will only be done by such cluster heads rather than allsensor nodes.

FIG. 1 illustrates an exemplary cluster head formation in LEACH. InLEACH, nodes are organized into local clusters, with one node acting asthe local base station (BS) or cluster-head 101 as seen in FIG. 1. Allthe other nodes (sensors) must transmit their data to the cluster heads(103), while the cluster-head nodes must receive data from all thecluster members, perform signal processing functions on the data (e.g.,data aggregation), and then transmit data to the remote base station.Because a cluster head is doing much more work and stays on all thetime, so being a cluster head is much more energy intensive than being anon-cluster head node. In order to evenly distribute the energy loadassociated with a cluster head and avoid draining the battery of any onesensor, cluster head position is rotated randomly among all the nodes.The medium access protocol in LEACH is also chosen to reduce energydissipation in non-cluster-head nodes. Since a cluster head node knowsall the cluster members, it can act as a local control center and createa TDMA schedule that allocates time slots for each cluster member. Indoing so, the LEACH incurs the advantageous ability of allowing thenodes to remain in the sleep state as long as possible. In addition,using a TDMA schedule prevents intra-cluster collisions.

While there are several advantages for using LEACH, this protocol offersno guarantee about the placement and/or number of cluster head nodes.Since the clustering process is adaptive, obtaining a poor clusteringsetup during a given round will not greatly affect overall performance.However, using a central control algorithm to form the clusters mayproduce better clusters by dispersing the cluster head nodes throughoutthe network. This is the basis for LEACH-centralized (LEACH-C). LEACH-Cis a protocol that uses a centralized clustering algorithm and the samesteady-state protocol as LEACH.

According to one embodiment, during the setup phase of LEACH-C, eachnode sends information about its current location (possibly determinedusing a GPS receiver) and energy level to the BS. In addition todetermining good clusters, the BS needs to ensure that the energy loadis evenly distributed among all the nodes. To do this, the BS computesthe average node energy, and whichever nodes have energy below thisaverage cannot be cluster heads for the current round. Using theremaining nodes as possible cluster heads, the BS finds clusters usingthe simulated annealing algorithm to solve the NP-hard problem offinding optimal clusters. This algorithm attempts to minimize the amountof energy for the non-cluster head nodes 105 to transmit their data tothe cluster head, by minimizing the total sum of squared distancesbetween all the non-cluster head nodes and the closest cluster head.

Once the cluster heads and associated clusters are found, the BSbroadcasts a message that contains the cluster head ID for each node. Ifa node's cluster head ID matches its own ID, the node is a cluster head;otherwise, the node determines its TDMA-slot for data transmission andgoes to sleep until it is time to transmit data. The steady-state phaseof LEACH-C is identical to that of LEACH.

The impact of sensors deployment on the WSN performance, lifetime andenergy consumption has been largely neglected. Accordingly, the presentembodiment describes intensive performance evaluations for differentsensor deployment distributions in WSN. FIGS. 2A-2D, depicts exemplaryfour 210-240 (grid, uniform, Normal and exponential) distributions,respectively.

FIG. 2A depicts a grid sensor distribution which represents thedeterministic distribution and may be used in several WSN applications,e.g. agricultural and environmental monitoring applications, due to itshigh performance in terms of network life, energy consumption and delay.In grid topology, the nodes are placed in such a way where the distancebetween any two adjacent nodes is the same. This makes clusteringcalculations easier than random distributions. However, many practicalWSN applications may not allow deterministic deployment for sensors,such as in disaster and military conditions. In such cases, otherdistributions (described below) which are drawn from naturally randomdistributions are more apt.

FIG. 2B depicts an exemplary uniform distribution of sensors in thegeographical area, whereas FIG. 2C depicts a Normal distribution ofsensors, where the majority of nodes are condensed at the center of thefield. The Normal distribution parameters are the same for bothdimensions i.e., the mean (μ_(x)=μ_(y)) is 50 (since the area is 100×100m²) and the standard deviation (σx=σy) is 25. The exponentialdistribution is shown FIG. 2D, with λ equals 35. In the exponentialdistribution the majority of the nodes are placed at the corner (bottomleft).

According to an embodiment, in order to investigate the impact of basestation location on the protocol performance (LEACH/LEACH-C) for thedistributions of FIGS. 2A-2D, two scenarios are considered: one wherethe base station is located in the center of the topology (i.e. (50,50)), and the other where the base station is located in the corner ofthe topology. Specifically, as shown in FIGS. 2A-2D, the base stationmay be located in one of 211, 221, 231, 241 (i.e., at the center) or213, 223, 233, and 243 (i.e., at the corner) respectively. In this way,by one embodiment, all possible combinations of the distributions withbase station locations are evaluated.

To characterize the packet delay, by one embodiment, two main delayparameters that affect the cluster based application performance areconsidered: the inter-cluster delay and intra-cluster delays, whereinthe inter-cluster delay is the delay that a packet suffers when it istransmitted from the cluster head to the base station. According toLEACH, a random access scheme is assumed. Hence, this delay component isunpredictable. On the other hand, the intra-cluster delay is the delaythat a packet suffers when it is transmitted from the sensor node to thecluster head. This delay component is deterministic astime-division-multiple-access (TDMA) is adopted.

FIGS. 3A-3D depict exemplary cluster formation 310-340 in the LEACH-Cprotocol (for 100 nodes with 5% cluster-heads) in a first round ofperformance evaluation for the four deployment strategies as depicted inFIGS. 2A-2D. It must be appreciated that there are significantdifferences in the way the sensor nodes are grouped into clusters,although all used LEACH as a cluster formation algorithm. For instance,using grid distribution, the size of clusters is more symmetric anduniform; while in case of exponential distribution, the majority of theclusters is located at the bottom left corner according to thedeployment parameter (i.e. λ_(x), λ_(y)) which will increase theprobability of collisions in that area. Although the other twodistributions (normal and uniform) almost have the same clusterdistribution, due to the chosen value of normal distribution standarddeviation, they differ in the cluster size which impacts theintra-cluster delay as is described later.

In contrast, increasing the percentage of cluster heads impliesdecreasing the cluster size, and leads to increasing the inter-clusterdelay due to the high probability of collision occurrence. In addition,the intra-cluster delay will decrease due to the small cluster size. Incontrast, decreasing the percentage of cluster heads decreases theprobability of collisions and consequently, decreases the inter-clusterdelay. However, this will be at the expense of increasing theintra-cluster delay due to larger cluster size compared to the previoussituation (large cluster heads number). This scenario may result indeferring the delivery of critical data as in the case of intrusiondetection network and cause inappropriate action. Therefore, it is atradeoff problem between two factors: inter-cluster delay andintra-cluster delay, as depicted in the graph 400 of FIG. 4, and thegoal is to operate at the optimal delay point 410 that minimizes thetotal delay.

According to one embodiment, in order to clarify the concept ofinter-cluster and intra-cluster delay and its impact, a simulationexample of a WSN with 100 nodes with 5% cluster heads for monitoringobject movement for security purposes is considered. In each round(simulation instant), different members in each cluster are considered,and such grouping is considered for the entire simulation run.Accordingly, a huge difference is observed among the clusters in termsof intra-cluster delay. Table I shows the size of clusters for eachdistribution and its corresponding delay components.

TABLE I cluster size and delay components for different deploymentdistributions. Cluster size and delay components for differentdeployment distributions. Upper right Upper left Bottom right Bottomleft corner cluster corner cluster corner cluster corner cluster Centralcluster Delay Cluster Delay Cluster Delay Cluster Delay Cluster DelayCluster size Intra Inter size Intra Inter size Intra Inter size IntraInter size Intra Inter Uniform 26 0.781 0.036 23 0.706 0.036 16 0.5290.036 23 0.706 0.036 12 0.428 0.036 Exponential 10 0.428 0.036 15 0.5040.036 16 0.529 0.036 33 0.956 0.036 26 0.732 0.036 Normal 11 0.403 0.03629 0.857 0.036 13 0.456 0.036 22 0.680 0.036 25 0.756 0.036 Grid 150.504 0.036 20 0.630 0.036 25 0.765 0.036 25 0.765 0.036 15 0.504 0.036

Referring to Table I, consider, for example, the exponential strategyand focus on the bottom left cluster (BLC) and upper right cluster(URC). If an event is detected in BLC, it takes about 33 time-slots todeliver the message to its cluster head, while in URC, it takes 10time-slots only. This instantaneous delay results in high delay jitterand failure in responding to the event in time.

Furthermore, from Table I it can be observed that the number of nodesbelonging to each cluster differs widely despite of using the samedeployment strategy. In one hand, this diversity results in orthogonaltransmissions among cluster heads and hence less contention to themedium. In consequence, as in Table 1, all inter-cluster delays are thesame for all distributions and corresponding clusters. On the otherhand, this result disappears when the cluster head percentage is high.

Additionally, the instantaneous intra-cluster delay varies with numberof cluster nodes and all are in range of hundreds of milliseconds. Thisalso shows the importance of decreasing this delay especially for realtime applications. It must be appreciated that this situation will lastfor the whole round. Furthermore, obtaining the average of inter-clusteror intra-cluster delay over the whole network should be avoided by oneembodiment, because it hides the instantaneous impact as illustratedbelow.

As LEACH tries to balance energy consumption among all nodes, thecluster formation changes periodically. Hence, we can compute theaverage intra-cluster delay by Eq. (1). Then, the cluster size ismultiplied by the TDMA slot time, which is constant for all nodes. Thus,from Eq. (1), the intra-cluster delay decreases as the number of clusterheads increases. For example, in cases of 5, 10, and 20, the averagedelay will be 20, 10, and 5 respectively, (multiplied by slot time).

$\begin{matrix}{{{Average}\mspace{14mu}{cluster}\mspace{14mu}{size}} = {\frac{{{No}.\mspace{14mu}{of}}\mspace{14mu}{nodes}}{{{No}.\mspace{14mu}{of}}\mspace{14mu}{cluster}\mspace{14mu}{heads}}.}} & (1)\end{matrix}$

On the other hand, the inter-cluster delay increases as number ofcluster heads increases. That is because the probability of collisionsin CSMA increases as number of senders (cluster heads) increases, due tothe high contention on the channel; as a result, the delay dramaticallyincreases. LEACH algorithm and in order to minimize interference fromconcurrent transmissions from different cluster heads, it uses a simplespreading mechanism where the spreading factor is equal to the number ofcluster heads plus one. For example, in case of 5, 10, 20, the averagedelay obtained by our simulation for grid distribution was, about 36,122, 9000 ms, respectively. Thus, the cluster head number is animportant design parameter that significantly affects the networkperformance in terms of delay and throughput.

According to an embodiment of the present disclosure, in order toevaluate the performance of wireless sensor networks under the LEACH andLEACH-C protocols, first is evaluated the energy efficiency of these twoprotocols, followed by their performance with respect to different dataloads, and finally the effect of the cluster size, number of clusterheads, and number of nodes on the inter and intra-cluster delays isinvestigated.

By one embodiment, in order to evaluate the WSNs, the NS-2 simulator isutilized. Considering the availability of data for transmission in eachsensor node, is emulated this phenomenon by forcing the sensor node tosleep 0%, 25%, 50%, and 75% of the TDMA frame cycle, where 0% means thatthe entire time slots are occupied with signals, i.e., none of them areempty. The energy model and other simulation parameters are summarizedbelow in Tables II and III.

TABLE II simulation parameters. Simulation parameters. Parameter ValueSimulation time 500 s Number of nodes 50, 100, 150, 200, 250 Simulationarea 100 × 100 m² Number of runs per scenario 10 times Base stations'positions Corner (5, 5) & Center (50, 50) Number of cluster heads 5% ofnumber of nodes Round time 50 s Data signal size 525 bytes Channel BW 1Mbps

TABLE III Energy model parameters. Energy model parameters. ParameterValue Initial energy 5 J Electronics energy 50 nJ/bit Receive threshold1 nJ Success threshold 6 nJ Data aggregation energy 5 nJ/bit/signal

By one embodiment, in order to evaluate the performance with differentnetwork conditions, different number of nodes to represent the sparse(light load, 50 nodes) and dense networks (heavy load, 250 nodes) areselected. Further, in order to measure the performance of LEACH andLEACH-C, the ratio of total delivered packets to the base station to thetotal energy consumption (packet/joule) is computed. The metric is morepractical that the typical measure (i.e. total packets or total energy)as it combines two measures in one and gives how much energy (includingrouting exchanged information packets, cluster formation packets, etc.)should be invested to get a data packet at the base station.Additionally, to ensure high confidence in the obtained results, foreach point in the curves (described below), ten random topologies foreach distribution are developed and then averaged to obtain the finalresults.

In what follows is described a performance comparison of the LEACH andLEACH-C routing protocols for varying sensor deployments. For sake ofclarity, the following abbreviations are used herein: leachCnNd-Leach,center BS and normal distribution, leachCrNd-Leach, corner BS and normaldistribution, leachCnUd-Leach, center BS and uniform distribution,leachCrUd-Leach, corner BS and uniform distribution, leachCnEd-Leach,center BS and exponential distribution, leachCrEd-Leach, corner BS andexponential distribution, leachCnGd-Leach, center BS and Griddistribution, and leachCrGd-Leach, corner BS and Grid distribution.

According to one embodiment, the following simulation results areobserved: determining the impact of different random distributions onLEACH where the base station is located either at the center or at thecorner on energy consumption assuming exhaustive data transmission.Further, the energy efficiency for the routing protocols under differentdata rates for the sensor nodes is evaluated, followed by the effect ofdifferent deployment distributions on the inter/intra-cluster delays.

Table IV summarizes the improvement over uniform distribution ofsensors. The presented numbers are normalized values compared to theperformance under uniform assumption. The minus sign (−) indicatesperformance degradation, whereas the positive sign (+) indicatesperformance improvement compared to uniform distribution. It can beobserved that on average the improvement is much more than thedegradation, for example the improvement can reach as high as 42%, and66% in case of normal and grid distributions, respectively.

TABLE IV comparison of sensor deployment strategies. Exponential NormalGrid No. of nodes CrBS CnBS CrBS CnBS CrBS CnBS 50 25% −24% 35% 18% 66%−29% 100 −9% 23% −16% −1% −8% −11% 150 18% 12% 42% 21% 55% 5% 200 −15%−2% −31% 12% 19% 91% 250 −18% −29% −3% −18% 10% −7% LEACH - Improvementcompared to uniform deployment; CrBS: the base station is located in thecorner, CnBS: the base station is located in the corner.

In contrast, considering LEACH-C routing protocol, we can observe itsconsistency in achieving better performance as shown in FIGS. 5 and 6.FIG. 5 depicts an exemplary bar graph depicting the performance of LEACHwith different sensor distributions and base station locations and FIG.6 depicts an exemplary graph depicting the performance of the LEACH-Cwith different sensor distributions and base station locations.

In FIG. 5 the bars 510-580 correspond to the performance of leachCrGd,leachCnNd, leachCnEd, leachCrUd, leachCrEd, leachCrNd, leachCnUd, andleachCnGd.

Moreover, LEACH-C always outperforms LEACH due to the centralizedclustering algorithm in LEACH-C. For example, for 50-node topology,LEACH-C can deliver around 700 packets per joule; whereas in case ofLEACH, the maximum is around 300 packets per joule which is nearly halfof LEACHC. This result can be attributed to the centralized clusterheads selection which yields better load balancing over network nodes.Also, in both protocols as we increase the number of nodes theperformance degrades, that is due to the increase of data collisions andretransmissions. However, in some cases such as LEACH uniformdistribution, the best case was in 100 nodes where the networkapproaches its peak performance.

Table IV shows that the location of base station plays a key role in theoverall performance. Tables IV and V illustrate the performancecomparison for the three deployment strategies (Normal, Grid andExponential) compared with uniform deployment strategy for LEACH andLEACH-C, respectively. It can be observed that there is a performancediscrepancy between LEACH and LEACH-C. For LEACH, grid topologies haveshown the best energy utilization compared to other random distributionswhen the base station is located at the corner of the monitored area,while it shows the worst performance when the base station is located inthe center except when the number of nodes is 200. This result can beexplained as follows: since LEACH is a localized approach and the gridtopology inherently has a balanced structure, the local decision onselecting the cluster head node and its children is optimized comparedto uniformly distributed nodes which may force LEACH to build unbalancedclusters as shown in FIG. 3B. Accordingly, locating the base stationnode near the center of the monitored area will be in favor of uniformlydistributed nodes that leads into higher throughput per joule comparedto grid distributed nodes. Consider the case of exponentiallydistributed topologies, locating the base station at the corner of thenetwork shows a clear improvement compared to uniform distribution. Thisresult is expected as most of the nodes are concentrated at the corneras shown in FIG. 2(d). However, the result is for the case of normallydistributed topologies illustrates outstanding performance when the basestation is located at the corner for 50 and 150 topologies. Theseresults indicate the huge impact the assumed topology distribution hason the energy utilization. In addition, these results show the instableperformance of LEACH.

TABLE V Performance improvement in LEACH-C. Exponential Normal Grid No.of nodes CrBS CnBS CrBS CnBS CrBS CnBS 50 39% 1% 42% −9% −64% 0% 100 34%−1% 44% −13% −73% 0% 150 37% −1% 43% −18% −64% −1% 200 55% −20% 35% −18%−70% 11% 250 19% −3% 23% −24% −87% 0% LEACH-C - Improvement compared touniform deployment; CrBS: the base station is located in the corner,CnBS: the base station is located in the corner.

Again, LEACH-C illustrates its superiority compared to LEACH when wecompare different topologies against the location of the base stationnode. On one hand, we can observe consistent improvement for normallyand exponentially distributed topologies when the base station islocated in the corner. On the other hand, the grid topology performancedegraded severely and it even showed lower than LEACH in terms of packetper joule. In addition, when the base station is placed at the center,LEACH-C seems to be optimized for uniformly distributed topologies andother topologies show no improvement or even lower performance. Theseresults show the importance of carefully selecting the topology and thedeployed routing protocol.

In the above embodiment, it was assumed that the sensor node always hasdata to transmit. Nonetheless, in real life applications, thisassumption might not be true where the data rate varies from node tonode based on several reasons such as the monitored event, and themonitored area. For example, in surveillance applications, sensor nodesdo not send anything unless an object intruding the monitored area isdetected. According to one embodiment, we consider variable data ratefor sensor nodes, and study the performance of LEACH and LEACH-C forfour different data rates. In our simulation experiments, we mimic thedata rate variation by forcing a number of nodes corresponding to theactual data rate to sleep during their reserved TDMA slots. Hence, weexpect LEACH routing protocol not to perform well since many slots willnot be utilized while the cluster head node is active waiting for datato be received.

FIGS. 7A-7D depicts exemplary graphs 710-740 depicting average packetenergy for different data rates for LEACH and LEACH-C. In FIGS. 7A-7D,the curves 701, 721, 731 and 741 correspond to 100% data rate, curves703, 723, 733, and 743 correspond to 75% data rate, curves 705, 725,735, and 745 correspond to 50% data rate, and the curves 707, 727, 737and 747 correspond to 25% data rate respectively.

FIGS. 7A and 7B depict the performance of LEACH for exponentiallydistributed topologies under different data rates. Similarity, FIGS. 7Cand 7D show the energy consumption efficiency under LEACH-C for centeredbase station and cornered base station, respectively. LEACH-C behaves ina similar manner compared to LEACH but LEACH-C is more consistent andthat is obvious from the results in Table 7, where there is no presencefor negative signs.

It can be observed that there is a high drop in derived data compared to100% activity case. Of course, as the node is only 25% active, we mayexpect the delivered data to drop by 75%. However, the actual drop isabout 90%. Again, as we noted above that LEACH can behave unpredictably.For example, for the case of 75% activity and the base station islocated in the center, the delivered packet per joule is higher than the150% case. This behavior is depicted in Table VI by the negative signs.

From Tables VI and VII, we can observe the following. First, in general,the data drop for centered base station is worse than the case when thebase station is located in the corner. Second, the higher the number ofnodes in the monitored area, the lower is the drop in received data.This result could be explained as follows. We have shown in the previousfigures as when the number of nodes increases the energy utilizationefficiency decreases due to the high likelihood of collision. Now, whenwe decrease the data rate, we actually have decreased the overallactivity of the network and hence, less collision would occur.Therefore, the energy utilization efficiency is expected to be increasedand this is what has been shown in Tables VI and VII.

TABLE VI efficiency drop compared to 100% in LEACH for exponentialdistribution. Drop in efficiency compared to 100% under LEACH withdifferent data rates and exponential sensor nodes deployment. Data rate25% Data rate 50% Data rate 75% No. of nodes CrBS CnBS CrBS CnBS CrBSCnBS 50 90% 91% 80% 76% 51% 33% 100 77% 75% 48% 53% 32% 15% 150 82% 64%61% 33% 28% −20% 200 53% 46% 11% −61% −13% −66% 250 52% 26% −13% −29%−58% −62%

TABLE VII efficiency drop compared to 100% in LEACH-C for exponentialdistribution. Drop in efficiency compared to 100% under LEACH-C withdifferent data rates and exponential sensor nodes deployment. Data rate25% Data rate 50% Data rate 75% No. of nodes CrBS CnBS CrBS CnBS CrBSCnBS 50 75% 77% 73% 73% 26% 24% 100 87% 88% 59% 59% 19% 17% 150 75% 76%61% 61% 33% 30% 200 80% 79% 58% 56% 28% 28% 250 77% 76% 60% 58% 33% 31%

In what follows is described the delay simulation results for theaverage delay followed by the delay behavior for the differentdistributions. FIG. 8 depicts according to an embodiment, an exemplarygraph 800 illustrating average inter and intra-cluster delay fordifferent sensor distributions. The curves 801, 803, 805 and 807correspond to the performance of exponential distribution-intra clusterdelay, grid distribution-intra cluster delay, grid distribution-intercluster delay, and exponential distribution-inter cluster delayrespectively.

FIG. 8 shows the difference of inter-cluster and intra-cluster delays incase of 5% number of cluster heads. As discussed previously, theinter-cluster delay is smaller than intra-cluster delay in case of smallpercentage of cluster heads, since lower rate of collision is expected.As the network becomes denser, the interference increases, therebycollisions increase; that it is clearly illustrated by FIG. 8 where thedelays of both inter and intra increase as number of nodes increases.The delay increment of intra-cluster is slower than inter because of thecollision free nature of TDMA, used in intra-cluster scheduling.Moreover, the grid distribution slightly outperforms exponentialdistribution in case of inter-cluster delay due to it is deterministicbehavior.

FIG. 9 depicts according to another embodiment, an exemplary graph 900illustrating average inter and intra-cluster delay for different sensordistributions. The curves 901, 903, 905 and 907 correspond to theperformance of exponential distribution-inter cluster delay, griddistribution-inter cluster delay, exponential distribution-intra clusterdelay, and gris distribution-intra cluster delay respectively.

FIG. 9 shows the effect of increasing the number of cluster heads onboth the intra-cluster and inter-cluster delays. The impact issignificant in case of inter delay due to increasing collisionprobability as number of cluster heads increases. It is interesting tonote that the situation is reversed compared to 5% and the inter delayis much greater than the intra delay components. And still the griddistribution shows better performance than exponential distribution. Incontrast to FIG. 8, this figure shows significant increasing of interdelay where it reaches approximately 14 s (unacceptable delay oncritical and real time systems) in case of 250 nodes. From both figures,we can see the effect of increasing the number of cluster heads; wherethe inter delay has the major effect when it turns from very low such as0.3 s in case of 50 nodes with 5% cluster heads, into very high delay incase of 20% cluster heads, where it reaches exactly 14.4 s in case of250 nodes with exponential distribution. As discussed before that resultreflects the problem of CSMA in case of inter-cluster communication dueto its random back-off and high contention period.

Having discussed the average delay performance for both inter-clusterdelay and intra-cluster delay, it is observed that LEACH-C has performedbetter in balancing the delay among all nodes and clusters. However, thereal time applications are concerned more with the instantaneousbehavior of the individual node or cluster. Therefore, using thecumulative distribution function (CDF), is described herein below, thestatistical behavior of both delay components (i.e. inter and intra)based on the collected samples from all random topologies.

Considering FIGS. 10-12, we make the following observations. Firstly,the intra-cluster delay is limited to 1.4 s while the inter-clusterdelay can extend as long as 45 s for large number of cluster heads.Secondly, the delay relation is not linear with respect to the number ofcluster heads. This is clearly shown in FIGS. 11 and 12 where for thecase of 3% and 5% cluster heads, the inter delay does not exceed 0.2 s,while for 15% and 20%, the inter delay is greater than 10 s for about10% and 40% of the simulation time, respectively.

Third, for both delay components, we can notice that the larger thenumber of cluster heads, the larger is the delay. This result especiallyfor the intra-cluster delay may contradict the discussion above where weargued that the smaller the cluster heads, the larger is theintra-delay. Here, it is worth to remind the reader that in LEACH andLEACH-C, the spreading factor is proportional to the number of clusterheads. Hence, the TDMA slot will increase proportional to the number ofcluster heads. In fact, this conservative design would lead to excessivedelay that will affect drastically the real time applications such assecurity applications.

Accordingly, by one embodiment, the spreading factor is fixed to 8 forthe 10%, 15% and 20% cases, while we keep it as is for 3% and 5%. FIG.13 illustrates the new CDF results. It is clear that the situation isthe opposite of what is depicted in FIG. 10 and the minimumintra-cluster delay occurs at 20% case. In addition, the maximumintra-cluster delay for all cases does not exceed 1.2 s compared to 3 onthe original LEACH. However, the inter delay is still increasing as thenumber of cluster heads increases and this is due to the CSMA protocol.

The huge demand for efficient and practical deployment of wirelesssensor networks pushes towards revisiting the existing protocols lookingfor better understanding and novel solutions. The above embodiments isone step in this direction where the impact of different sensor nodesdeployments is evaluated and the behavior of routing protocols such asLEACH and LEACHC is characterized. Furthermore, embodiments describedherein investigate the performance of LEACH and LEACH-C for differentdata rate availability which emulates real applications where there isno exhaustive data transmission. Furthermore, the above embodimentinvestigate the cluster formation effect on the overall system delay andwe discussed the relationship between the inter-cluster delay, theintra-cluster delay and the system parameters such as the number ofcluster heads and spreading factor.

Each of the functions of the described embodiments may be implemented byone or more processing circuits. A processing circuit includes aprogrammed processor (for example, processor 1403 in FIG. 14), as aprocessor includes circuitry. A processing circuit also includes devicessuch as an application-specific integrated circuit (ASIC) and circuitcomponents arranged to perform the recited functions The variousfeatures discussed above may be implemented by a computer system (orprogrammable logic). FIG. 14 illustrates such a computer system 1401.

The computer system 1401 includes a disk controller 1406 coupled to thebus 1402 to control one or more storage devices for storing informationand instructions, such as a magnetic hard disk 1407, and a removablemedia drive 1408 (e.g., floppy disk drive, read-only compact disc drive,read/write compact disc drive, compact disc jukebox, tape drive, andremovable magneto-optical drive). The storage devices may be added tothe computer system 1401 using an appropriate device interface (e.g.,small computer system interface (SCSI), integrated device electronics(IDE), enhanced-IDE (E-IDE), direct memory access (DMA), or ultra-DMA).

The computer system 1401 may also include special purpose logic devices(e.g., application specific integrated circuits (ASICs)) or configurablelogic devices (e.g., simple programmable logic devices (SPLDs), complexprogrammable logic devices (CPLDs), and field programmable gate arrays(FPGAs)).

The computer system 1401 may also include a display controller 1409coupled to the bus 1402 to control a display 1410, for displayinginformation to a computer user. The computer system includes inputdevices, such as a keyboard 1411 and a pointing device 1412, forinteracting with a computer user and providing information to theprocessor 1403. The pointing device 1412, for example, may be a mouse, atrackball, a finger for a touch screen sensor, or a pointing stick forcommunicating direction information and command selections to theprocessor 1403 and for controlling cursor movement on the display 1410.

The processor 1403 executes one or more sequences of one or moreinstructions contained in a memory, such as the main memory 1404. Suchinstructions may be read into the main memory 1404 from another computerreadable medium, such as a hard disk 1407 or a removable media drive1408. One or more processors in a multi-processing arrangement may alsobe employed to execute the sequences of instructions contained in mainmemory 1404. In alternative embodiments, hard-wired circuitry may beused in place of or in combination with software instructions. Thus,embodiments are not limited to any specific combination of hardwarecircuitry and software.

As stated above, the computer system 1401 includes at least one computerreadable medium or memory for holding instructions programmed accordingto any of the teachings of the present disclosure and for containingdata structures, tables, records, or other data described herein.Examples of computer readable media are compact discs, hard disks,floppy disks, tape, magneto-optical disks, PROMs (EPROM, EEPROM, flashEPROM), DRAM, SRAM, SDRAM, or any other magnetic medium, compact discs(e.g., CD-ROM), or any other optical medium, punch cards, paper tape, orother physical medium with patterns of holes.

Stored on any one or on a combination of computer readable media, thepresent disclosure includes software for controlling the computer system1401, for driving a device or devices for implementing the invention,and for enabling the computer system 1401 to interact with a human user.Such software may include, but is not limited to, device drivers,operating systems, and applications software. Such computer readablemedia further includes the computer program product of the presentdisclosure for performing all or a portion (if processing isdistributed) of the processing performed in implementing any portion ofthe invention.

The computer code devices of the present embodiments may be anyinterpretable or executable code mechanism, including but not limited toscripts, interpretable programs, dynamic link libraries (DLLs), Javaclasses, and complete executable programs. Moreover, parts of theprocessing of the present embodiments may be distributed for betterperformance, reliability, and/or cost.

The term “computer readable medium” as used herein refers to anynon-transitory medium that participates in providing instructions to theprocessor 1403 for execution. A computer readable medium may take manyforms, including but not limited to, non-volatile media or volatilemedia. Non-volatile media includes, for example, optical, magneticdisks, and magneto-optical disks, such as the hard disk 1407 or theremovable media drive 1408. Volatile media includes dynamic memory, suchas the main memory 1404. Transmission media, on the contrary, includescoaxial cables, copper wire and fiber optics, including the wires thatmake up the bus 1402. Transmission media also may also take the form ofacoustic or light waves, such as those generated during radio wave andinfrared data communications.

Various forms of computer readable media may be involved in carrying outone or more sequences of one or more instructions to processor 1403 forexecution. For example, the instructions may initially be carried on amagnetic disk of a remote computer. The remote computer can load theinstructions for implementing all or a portion of the present disclosureremotely into a dynamic memory and send the instructions over atelephone line using a modem. A modem local to the computer system 1401may receive the data on the telephone line and place the data on the bus1402. The bus 1402 carries the data to the main memory 1404, from whichthe processor 1403 retrieves and executes the instructions. Theinstructions received by the main memory 11404 may optionally be storedon storage device 1407 or 1408 either before or after execution byprocessor 1403.

The computer system 1401 also includes a communication interface 1413coupled to the bus 1402. The communication interface 1413 provides atwo-way data communication coupling to a network link 1414 that isconnected to, for example, a local area network (LAN) 1415, or toanother communications network 1416 such as the Internet. For example,the communication interface 1413 may be a network interface card toattach to any packet switched LAN. As another example, the communicationinterface 1413 may be an integrated services digital network (ISDN)card. Wireless links may also be implemented. In any suchimplementation, the communication interface 1413 sends and receiveselectrical, electromagnetic or optical signals that carry digital datastreams representing various types of information.

The network link 1414 typically provides data communication through oneor more networks to other data devices. For example, the network link1414 may provide a connection to another computer through a localnetwork 1415 (e.g., a LAN) or through equipment operated by a serviceprovider, which provides communication services through a communicationsnetwork 1416. The local network 1414 and the communications network 1416use, for example, electrical, electromagnetic, or optical signals thatcarry digital data streams, and the associated physical layer (e.g., CAT5 cable, coaxial cable, optical fiber, etc.). The signals through thevarious networks and the signals on the network link 1414 and throughthe communication interface 1413, which carry the digital data to andfrom the computer system 1401 may be implemented in baseband signals, orcarrier wave based signals.

The baseband signals convey the digital data as unmodulated electricalpulses that are descriptive of a stream of digital data bits, where theterm “bits” is to be construed broadly to mean symbol, where each symbolconveys at least one or more information bits. The digital data may alsobe used to modulate a carrier wave, such as with amplitude, phase and/orfrequency shift keyed signals that are propagated over a conductivemedia, or transmitted as electromagnetic waves through a propagationmedium. Thus, the digital data may be sent as unmodulated baseband datathrough a “wired” communication channel and/or sent within apredetermined frequency band, different than baseband, by modulating acarrier wave. The computer system 1401 can transmit and receive data,including program code, through the network(s) 1415 and 1416, thenetwork link 1414 and the communication interface 1413. Moreover, thenetwork link 1414 may provide a connection through a LAN 1415 to amobile device 1417 such as a personal digital assistant (PDA) laptopcomputer, or cellular telephone.

While aspects of the present disclosure have been described inconjunction with the specific embodiments thereof that are proposed asexamples, alternatives, modifications, and variations to the examplesmay be made. It should be noted that, as used in the specification andthe appended claims, the singular forms “a,” “an,” and “the” includeplural referents unless the context clearly dictates otherwise.

What is claimed is:
 1. A method of operating a computer system todetermine the performance of a wireless sensor network including aplurality of sensors, the method comprising: selecting, a sensordistribution pattern for a geographical region where the sensors are tobe deployed; determining a location for a base station in thegeographical region; generating by circuitry, a plurality of sensorclusters, each sensor cluster of the plurality of sensor clusters beingformed by one of a first grouping mechanism and a second groupingmechanism, the first grouping mechanism forming the sensor cluster basedon a strength of a signal transmitted by each sensor, that is receivedby the base station, and the second grouping mechanism forming thesensor cluster based on a location of the sensor and an energy level ofthe sensor; allocating, for each sensor included in the generated sensorcluster, a time-slot within a time-frame corresponding to the sensorcluster, the time-slot being utilized for transmitting a data packetfrom the sensor to the base station; and evaluating by the circuitry,the performance of the first grouping mechanism and the second groupingmechanism for the selected sensor distribution pattern and base stationlocation, by computing at least a ratio of delivered data packets to thebase station to a total energy consumption, and a first delay and asecond delay incurred by each data packet, wherein the first delay is anaverage intra-cluster delay of from 0.2 to 1 second and the second delayis an average inter-cluster delay of less than 20 seconds, wherein theselected sensor distribution pattern is a grid pattern wherein thesensors are disposed in a manner such that a distance between adjacentsensors is a predetermined distance, in a normal distribution pattern aprinciple number of sensors are disposed in the center of thegeographical region, and in a exponential distribution pattern, aprinciple number of sensors are disposed in the corner of thegeographical region.
 2. The method according to claim 1, wherein thelocation for the base station in the geographical region is one of acenter of the geographical region, and a corner of the geographicalregion.
 3. The method according to claim 1, wherein the generating stepfurther comprises: computing by the circuitry, for the second groupingmechanism, an average sensor energy corresponding to the sensors in thegeographical region; generating a non-cluster sensor group includingsensors that have energy lower than the computed average sensor energy;and forming the sensor clusters based on a simulated annealingalgorithm.
 4. The method according to claim 1, further comprising:assigning for each generated sensor cluster, a cluster-head sensor, thecluster head sensor receiving data from other sensors in the sensorcluster and transmitting the received data to the base station.
 5. Themethod according to claim 3, wherein the forming step further comprises:minimizing a total sum of squared distances between sensors included inthe non-cluster sensor group and their respective cluster head-sensor.6. The method according to claim 1; further comprising: re-assigning bythe circuitry, after a predetermined time-interval, for each generatedsensor cluster, the cluster head-sensor.
 7. The method according toclaim 1, wherein the evaluating step further comprises: determining, foreach sensor in the geographical region, availability of data to betransmitted to the base station; and de-activating the sensor in itsallocated time-slot based on no data being available for transmission tothe base station in the time-slot.